Research: flag-43 I−G/2 side correction at #3508 co-hosted cut costs +2 rank mass (no new kappa)

[VictorLiwentao]

Change and scope

Bounded follow-up under priority revision 6, card p104-side-correction. Merged #3508 gives a zero-added-mass head-step repair R0 for flag 43 and leaves open the cost of the I − G/2 side correction at the co-hosted chart. This package answers that OQ for entry (59,21) (G[59,21]=1 ⇒ add −1/2·X21 into Y59).

On R0, four concrete corrections replace Y59's terminal transport at 3525 while the head is still co-hosted (Y59 in W6, X21 in FULL, both spanning 15):

Word	Δ transports	Δ ADDs	Δ rank mass	Profile Δ vs R0
T (target lift W6→FULL, ADD, descend)	+1	+1	+2	H1 − H2 + H3
S (source detour FULL→F59→FULL)	+2	+1	+2	2H1
P (one private-copy lifetime)	+1	+1	+1	H1
T48 (whole row 59 on T's lift)	+1	+48	+2	H1 − H2 + H3

Native check_native.validate() passes each coefficient-0 word (incl. two new FULL ↔ F59 recipes). Real words fail only at Y59's endpoint; only Y59 changes.

Obstruction (class Z = #3508’s). Zero added rank mass is impossible for all 28 insertion placements: events 625/884 force head 131 of X12 into X21; G[59,12]=0 keeps 131 outside Y59's final; added non-private mass is even ⇒ strict min +2. The published end-cut detour also costs +2, so co-host discount = 0. P’s +1 needs an inherited private-copy discard (admissibility left open; strict bill remains +2 if discard is disallowed).

Scoped bill. No new kappa. Selected κ stays 0.001672660197076918.

Result

Package: research/p104-flag43-side-correction-bill/.
Tip: 26394881f0a183ca0df3d986ec58aa56900ada6c.
Content tip: 8838ce9049e3c0beb555b8e1b6d48c9e11be3685.
Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90 (required after #3508 merge; 6f100d4bb is an ancestor).

Validation

python3.12 -I -B research/p104-flag43-side-correction-bill/verify.py
python3.12 -I -O -Werror -B research/p104-flag43-side-correction-bill/verify.py
python3.12 -I -O -Werror -B research/p104-flag43-side-correction-bill/independent.py
python3.12 -I -O -Werror -B research/p104-flag43-side-correction-bill/test_package.py
python3.12 -B scripts/research_package.py --package research/p104-flag43-side-correction-bill

Expected:

PASS_P104_FLAG43_SIDE_CORRECTION_BILL flag=43 entry=(59,21) coefficient=-1/2 zero_mass_placements=0/28 … strict_min_added_rank=2 … cohost_discount=0 native_validate=4/4 no_new_kappa
PASS_P104_FLAG43_SIDE_CORRECTION_BILL_INDEPENDENT … rows_changed=Y59_only … no_new_kappa
PASS_P104_FLAG43_SIDE_CORRECTION_BILL_TESTS cases=14 clean_read_only=1 scanners=2
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-flag43-side-correction-bill outcome=completed

Default verify is read-only. Admission uses need() and still fires under -O.

Overlap and credit

Closest priors: #3508 (R0 + OQ2), #3456 (chronology, cited only), research/p104-side-correction-rank-obstruction (end-cut +2; this package’s novelty is co-hosted placement, 0/28 obstruction + forcing chain, P route, native validation). Soft-overlap checked against open #3532 (flag 1; untouched). Does not reopen deferred repair clones, #3441/#3436/#3421/#3411, or the merged readout series through #2883.

Credit #3508, #3456, the side-correction-rank-obstruction authors, Nick Petalas / #2981, and Chafik Boukhalfa. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.